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January 2025 term · Statistics for Data Science II · BSMA1004

Statistics for Data Science II Quiz 2: 16 March 2025 (January 2025 term)

The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term: 16 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
16
Marks
40
Duration
120 min
MCQ
7
MSQ
2
Numerical
7
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN EXAM QDD2 16 Mar 2025 · No negative marking.

Question 1

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 1 on its own page

Question 2

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 2 on its own page

Question 3

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 3 on its own page

Question 4

+3 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • B
  • D
Question 4 on its own page

Question 5

+1 markOne correct option

Wires produced from a factory have a mean breaking strength of 50 kilograms with a standard deviation of 4 kilograms. In a statistical study of breaking strength of these wires, suppose the sample size is increased from 81 to 144.
Based on the above data, answer the given subquestions.

How does the expected value of the sample mean change?

  1. A

    The expected value decreases.

  2. B

    The expected value increases.

  3. C

    The expected value remains the same.

  4. D

    The expected value fluctuates randomly.

Show answer

Correct answer

  • C

    The expected value remains the same.

Question 5 on its own page

Question 6

+2 marksOne correct option

Wires produced from a factory have a mean breaking strength of 50 kilograms with a standard deviation of 4 kilograms. In a statistical study of breaking strength of these wires, suppose the sample size is increased from 81 to 144.
Based on the above data, answer the given subquestions.

How does the variance of the sample mean change?

  1. A

    Variance is reduced from 0.049 to 0.027

  2. B

    Variance is reduced from 0.198 to 0.111

  3. C

    Variance is increased from 0.111 to 0.198

  4. D

    Variance remains the same.

Show answer

Correct answer

  • B

    Variance is reduced from 0.198 to 0.111

Question 6 on its own page

Question 7

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the value of E[X]. Enter the answer correct to two decimal places

Show answer

Correct answer: 0.42 (accepted within ±0.03)

Question 7 on its own page

Question 8

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

What is the value of Var(X)? Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.08 (accepted within ±0.03)

Question 8 on its own page

Question 9

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Find the value of k.

Show answer

Correct answer: 4

Question 9 on its own page

Question 10

+3 marksOne correct option

Based on the above data, answer the given subquestions.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 10 on its own page

Question 11

+2 marksOne or more correct options

Based on the above data, answer the given subquestions.

Which of the following option(s) is(are) correct ?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • D
Question 11 on its own page

Question 12

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Using Chebyshev’s inequality, find a lower bound for P(|Y −0.5| < 0.6). Enter the answer correct to three decimal places.

Show answer

Correct answer: 0.977 (accepted within ±0.004)

Question 12 on its own page

Question 13

+4 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.75 (accepted within ±0.03)

Question 13 on its own page

Question 14

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0

Question 14 on its own page

Question 15

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Which of the following options is an acceptable approximate model for S as per the Central Limit Theorem?

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 15 on its own page

Question 16

+3 marksNumerical answer

Based on the above data, answer the given subquestions.

Using the Central Limit Theorem, find an approximate probability that the total number of heads, S, lies between 48 and 52 heads. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.31 (accepted within ±0.03)

Question 16 on its own page